A quick look at the generalistion of the sum & difference formulae

Topic: sum & difference formulae

General expressions for the factorising and expanding of cubics

Topics: algebra, cubic

Differentiating a product of two functions

Topic: calculus

Investigating graphs through limits

Topics: limits, calculus

Converting the product of two trig functions inti a sum, and visa versa

Topic: trig

Using integration to find volumes

Topics: integration, volumes

Looking at the initial angle theorems.

Topics: circles, angle theorems, euclidean geometry

Describing the parabola geometrically and deriving the algebraic form.

Topics: parabola, locus

Using the derivative to solve rates of change problems

Topics: calculus, rates of change

Working with surds

Topic: surds

What if some of the objects are the same?

Topic: permutations

Looking at the relationship between the roots and coefficients ofa polynomial

Topic: polynomials

Reducing equations to quadratics in order to solve.

Topic: quadratic

looking at number patterns

Topic: series

Finding the means of numbers

Topics: series, means

Finding the area under a curve

Topics: integration, area

How to find the equation of a line that passes through the point of intersection of two given lines and another point.

Topics: linear function, lamda formula

Find the equaio ofthe chord of contact

Topic: parabola

Defining and proving the irrationality of numbers

Topic: irrational

Solving optimisation problems using calculus.

Topics: calculus, maxima, minima

Finding the equation of a line that pase through the intersection of two given lines and another point.

Topics: linear function, lamda formula

Using first principles to come up with a rule for differentiating polynomial functions.

Topics: calculus, differentiation

Inequalities are represented by regions when placed on the number plane.

Topics: algebra, curve sketching, inequalities

Deriving the equatiuon of te chord of contact

Topics: parabola, chord

Solving problems using calculus

Topic: calculus

Key features to look for when sketching polynomials

Topics: polynomials, curve sketching

Solving trig equations

Topics: trigonometry, trig equations

Introducing sigma notation

Topics: series, sum

Calculating areas if irregular shapes

Topics: integration, areas

Solving equations (and inequations)

Topics: equations, inequations

The basic algebraic operations

Topics: algebra, indices

Inequalities involving two variablss

Topic: regions

Defining functions and finding domain and range

Topics: functions, domain, range

Finally a look at the inequality type of induction problem

Topics: induction, inequality

Sketching polynomials by looking for key details in the equation

Topics: polynomial, curve sketching

Defining the quadratic and how to find its important features.

Topics: quadratic, curve sketching

Properties of quadrilaterals

Topics: geometry, quadrilaterals

Looking at the specific case of the locus as a parabola

Topics: parabola, locus

The basic definitions of circke properties and introducing some chord (arc) theorems.

Topics: euclidean geometry, circle, chord theorems

The alternate segment

Topic: alternate segment

Expanding on the idea of transforming the basic curves.

Topic: curve sketching

the primitive function

Topics: calculus, primitive function

Calculating a series

Topic: series

The properties of quadrilaterals become more specialised as you branch down the "family" tree.

Topics: geometry, quadrilaterals

When two quadrtics are "congruent", the coefficients an be matched.

Topics: quadratic, identities

The first of the angle theorems

Topic: circle geometry

Techniques for solving basic equations/

Topics: algebra, equations

Defining te sine rule for use in non-right angled triangles, as well as a formuls for finding the area of a triangle without having to know the perpendicular height.

Topics: trigonometry, sine rule, area

Three diferent levels of inequality questions

Topic: inequations

How to find areas for functions too difficult to integrate

Topic: integration

Deriving the sine rule

Topic: trigonometry

Looking at a couple of unusual questions

Topic: dynamics

Deriving the double angle formulae

Topics: trigonometry, double angles

A couple of questions that have appeared in the past years

Topic: induction

Newton's method

Topic: approximation

Finding the valueof integrals for curves that can't be integrated!!

Topics: integration, approximations

Some alternative ways of finding the features of quadratics

Topic: quadratic

Manipulating the roots of unity

Topics: complex numbers, roots of unity

Raising complex numbers to powers

Topics: complex numbers, de moivres

A regular question in the Extension 2 paper involves circle geometry

Topics: harder extension 1, circle geometry

Defining the family of conics and more specifically, te ellipse.

Topics: conics, ellipse

Sketching functions on the complex plane

Topics: complex numbers, locus

Defining the parametric coordinates of the ellipse and finding the tangent and normal.

Topics: conics, parmeters, ellipse

Lines & rays in the Argand diagram

Topics: complex numbers, locus

The parametric form of the ellipse

Topics: ellipse, parameters

Extending the relationship between roots & coefficients

Topic: polynomials

Factorising over rtge complex field

Topic: polynomials

Investigating roots of higher multiplicity

Topic: polynomials

Expanding on the idea from Extension 1

Topics: polynomials, roots, coefficients

Transforming a special hyperbola

Topic: hyperbola

The product rule for integration

Topics: integration, by parts

Sketching curves that are a composition of two (or more) functions.

Topic: curve sketching

A hyperbola whose asymptotes are perpendicular

Topics: conics, hyperbola

Expressing acceleration in different ways

Topic: acceleration

Investigating the forces involved in circular motion

Topic: circular motion